Similar issue. Early 2011 13" MBP, 2.3 ghz I5, 8GB, 256GB SSD,
No firewall, AT2 is up to date.
Airplay connects same way it worked with Mavericks and Yosemite.
After playing fine for 2-3 minutes, the audio stays good, but the video has bad frame rate,
(it is more like a collection of still images) and is 10+ seconds behind the audio.
after running this way for 20-30 minutes, it clears up to run flawlessly for a minute or two.
Then reverts back to the delayed, spotty, video with OK audio.
It shows constantly perfect on MBP screen which is being mirrored.
Same content connects and runs fine from similar capability Mini. (running Mavericks)